Minimal Surfaces in a Complex Projective Space Whose Mean Curvature Vectors Are Eigenvectors
نویسندگان
چکیده
B.Y. Chen Null 2-type surfaces in Euclidean space, Algebra, Analysis and Geometry, Taipei, World Scientiic 1989, 1-18] initiated the study of submanifolds whose mean curvature vector H is an eigenvector of the Laplacian. In this article, we study this problem for minimal surfaces in CP n. Two classiication theorems are obtained.
منابع مشابه
Pseudo Ricci symmetric real hypersurfaces of a complex projective space
Pseudo Ricci symmetric real hypersurfaces of a complex projective space are classified and it is proved that there are no pseudo Ricci symmetric real hypersurfaces of the complex projective space CPn for which the vector field ξ from the almost contact metric structure (φ, ξ, η, g) is a principal curvature vector field.
متن کاملIsotropic Lagrangian Submanifolds in Complex Space Forms
In this paper we study isotropic Lagrangian submanifolds , in complex space forms . It is shown that they are either totally geodesic or minimal in the complex projective space , if . When , they are either totally geodesic or minimal in . We also give a classification of semi-parallel Lagrangian H-umbilical submanifolds.
متن کاملThe Spinor Representation of Surfaces in Space
The spinor representation is developed for conformal immersions of Riemann surfaces into space. We adapt the approach of Dennis Sullivan 33], which treats a spin structure on a Riemann surface M as a complex line bundle S whose square is the canonical line bundle K = T(M). Given a conformal immersion of M into R 3 , the unique spin strucure on S 2 pulls back via the Gauss map to a spin structur...
متن کاملCharacterizations of Slant Ruled Surfaces in the Euclidean 3-space
In this study, we give the relationships between the conical curvatures of ruled surfaces generated by the unit vectors of the ruling, central normal and central tangent of a ruled surface in the Euclidean 3-space E^3. We obtain differential equations characterizing slant ruled surfaces and if the reference ruled surface is a slant ruled surface, we give the conditions for the surfaces generate...
متن کامل1 7 Fe b 20 05 Transforms for minimal surfaces in the 5 - sphere
We define two transforms between minimal surfaces with non-circular ellipse of curvature in the 5-sphere, and show how this enables us to construct, from one such surface, a sequence of such surfaces. We also use the transforms to show how to associate to such a surface a corresponding ruled minimal Lagrangian submanifold of complex projective 3-space, which gives the converse of a construction...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 1995